Would it be possible to get it purified enough so the boiling point would be feasible to build a fridge?

Interestingly yes,^1^ and also, countries went to war for it. Specifically guano and urea (not so much for refrigeration, but for gunpowder). It would be entirely reasonable, with the right skill-set, to concentrate ammonia.

As far as incorporating it into a refrigeration cycle, its basically the same as any other refrigerant in that your going to need a compression loop and an expansion loop to move heat from place A to place B. But lead lined clay or wood pipes could probably meet this requirement^2^.

The earliest ammonia based refridgerators (freezers really) were used almost exclusively for generating ice, which was then sold and moved to other places for refrigeration. Ice like many other staples became a daily sundry like milk or eggs. You can still find many of these "ice houses" all over the world, since they're not even that old. The town I grew up in had a club called the Ice House which was literally an old ice factory.

1: Another reference to the guano wars: https://thebreakthrough.org/articles/remember-the-guano-wars

2: History of early ammonia refrigerators: https://www.ashrae.org/file%20library/technical%20resources/ashrae%20journal/125thanniversaryarticles/60-68_boyle_historical-article-excerpt.pdf